Institution(s): 1. Nanjing University
We present the microscopic origin of the super strong magnetic fields in magnetars.
The ultra-strong magnetic field of the magnetars originates really from the induced paramagnetic moment of the 3P2 superfluid with significant mass more than 0.1m⊙ in a condition when their interior temperature here is the energy gap of the neutron 3P2 Cooper pairs. In the case, a phase transition from paramagnetism to ferromagnetism due to the induced paramagnetic moment of 3P2 Cooper pairs in the presence of background magnetic field. The upper limit of the magnetic field for the magnetars is .
2．We find that the electron Fermi energy, , increases with the magnetic field strength and it is proportional to . We note that this result is exactly the opposite of the popular idea that the electron Fermi energy decreases with the magnetic field. The key reason for the dilemma is that an incorrect formulae of the microscopic number of states for the electrons in intense magnetic field from some internationally well known popular textbooks on statistical physics has been repeatedly quoted by many authors.
3. We propose a new mechanism for the production of the high soft X-ray luminosities of magnetars. In particular, the Fermi energy of the electrons is higher than 60MeV in ultra-strong magnetic fields, B>> Bcr (=4.414´1013 gauss), which is much higher than the Fermi energy of the neutrons. In this case, the process of electron capture (EC) by protons around the proton Femi surface would dominate in magnetars. The outgoing high-energy neutrons due to EC process can easily destroy the Cooper pairs through the nuclear strong interaction. When one Cooper pair is destroyed, the orderly magnetic energy would be released and transformed into disorder thermal energy, then it may be radiated as soft X-rays. The Energy is in the X-ray – soft g-ray range. The total magnetic energy of Cooper pairs can be estimated as . This energy can maintain over yrs for of per magnetar. We have also calculated the theoretical luminosities of magnetars, and our results compared very well with observations of magnetars.